Science Behind The Butterfly Effect

Forty-five years ago, Ed Lorenz changed one thing. And that changed everything.

Lorenz, a researcher at the Massachusetts Institute of Technology, neglected to program his computer one afternoon to calculate results of a weather simulation in five digits. He wanted to see a sequence again and, as a shortcut, set the machine to generate results rounded out to only three digits.

Although the adjustment was tiny, chaos stepped in and the computer produced completely different forecasts than it had before. Lorenz's discovery would come to rock the scientific world: Some systems are so complex, even making the smallest change can lead to practically unpredictable results — or chaos.

Now swap the computer's churning to a young man's life and the programming tweak to going back in time and altering the past and you've got a Hollywood movie.

The Butterfly Effect, a film from New Line Cinema, starring Ashton Kutcher, takes its inspiration from Lorenz's subsequent analogy, "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" (Look for an adaptation of the quote at the start of the movie.)

But while Kutcher's movie character fails to grasp the concept of chaos as he repeatedly returns to the past to try and better his world, scientists are getting better at harnessing the power of chaos and Lorenz's so-called butterfly effect.

In fact, their work is leading to revelations in everything from weather prediction to managing alcoholism to gauging a marriage's success.

Using Chaos for the Weather Forecast

Bigger and better computers help when it comes to calculating chaos. Take, for example, Lorenz's field of weather prediction.

Weather is the result of some five million billion tons of air and water vapor churning around our planet. The interactions of so many moving parts are complex enough that, in some cases, even the proverbial flap of a butterfly's wing could possibly lead to a big weather change elsewhere.

To tackle that complexity, the National Weather Service now runs "ensemble forecasts," in which a computer model generates a model forecast and then several others that are each adjusted by slightly different factors. If the different forecasts end up being similar, meteorologists can forecast rain or snow or sun with high probability. If the forecasts don't agree, the probability rating drops.

The butterfly effect concept has also guided meteorologists to zero in on regions known as chaos hot spots to make weather predictions more accurate.

James Yorke, a math professor and chaos guru at the University of Maryland, recently led a team to identify these hot spots and showed these areas, which make up about 20 percent of the global map at one time, are more sensitive to small changes like the flapping of a butterfly wing.

By locating the perpetually shifting hot spots and taking good observations from them, meteorologists can get a step up on chaos and make better predictions.

Kerry Emanuel of the Massachusetts Institute of Technology in Cambridge, Mass., points out the finding sheds light on one caveat in Lorenz's butterfly theory.

"There are times and places where butterflies will make no difference," Emanuel said. "But in the right place and time, even a butterfly can alter the whole pattern of weather if you wait long enough."

Why Alcoholics Drink, Why Marriages Fail

The butterfly effect can alter much more than weather, let alone Hollywood plot lines. It's a general concept that applies to nearly any system that's complicated.

Michael Marder, a physicist at the University of Texas at Austin, uses it to understand the patterns that form on ocean floors by lapping waves and the stretch marks that are created in the texture of a plastic bag when it's ripped.

"Even studying the small things can tell you about the complexity of the real world," he said.

Others have tapped into the concepts of chaos to understand why alcoholics can't quit drinking. Last May, researchers at Ohio State University tracked the daily alcohol intake of a 40-year-old man over five years and found his sudden, irregular changes in behavior followed the chaos theory model.

And researchers at the University of Washington in Seattle recently found signs of a chaos in another highly complex system — marriage.

Mathematician John Murray and psychologist John Gottman examined 700 couples for over a decade. They recorded conversations early in each marriage and marked how many times they smiled, joked, raised their eyebrows or mocked each other. Then, using a set of equations based on a branch of math related to chaos theory, Murray estimated how long each couple would remain married.

"One equation incorporates how the wife will speak, depending on what the husband says, what her state of mind was before and so on. Then you have the equivalent equation of the husband. These two equations can generate chaotic solutions," Murray explained.

Using the equations, Murray said they predicted the success of each marriage 94 percent of the time.

It's the kind of number crunching that would have benefited Kutcher's character as he grapples with his power to alter history. Then again, as Marder points out, movie characters are ultimately guided by a whole different field of logic besides mathematics.

"All movies in the past have shown us if we were granted a wish to alter the past, we'd regret doing so," he said. "Those aren't just the rules of chaos, those are the rules of Hollywood."